% Mizar problem: t51_sublemma,sublemma,1188,5 
fof(t51_sublemma, conjecture,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [C] :  (m2_subset_1(C, k16_substut1(A), k38_substut1(A)) =>  (! [D] :  (m1_substut1(D, A, k7_sublemma(A, C, B)) =>  ( (v3_substut1(k7_sublemma(A, C, B), A) & r2_tarski(B, k10_xtuple_0(k7_substut1(A, B, k11_cqc_lang(A, B, k2_sublemma(A, C)), D))))  => k35_substut1(A, k32_substut1(A, k9_sublemma(A, k7_sublemma(A, C, B), D)))=k2_qc_lang3(A, k13_substut1(A, k7_substut1(A, B, k11_cqc_lang(A, B, k2_sublemma(A, C)), D), k2_sublemma(A, C)))) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (v1_relat_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(d35_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k16_substut1(A)) => k32_substut1(A, B)=B) ) ) ) ).
fof(d36_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k2_zfmisc_1(k9_qc_lang1(A), k1_substut1(A))) =>  ( (r2_tarski(k21_qc_lang1(A, k33_substut1(A, B)), k10_xtuple_0(k7_substut1(A, k21_qc_lang1(A, k33_substut1(A, B)), k33_substut1(A, B), k34_substut1(A, B)))) => k35_substut1(A, B)=k2_qc_lang3(A, k13_substut1(A, k7_substut1(A, k21_qc_lang1(A, k33_substut1(A, B)), k33_substut1(A, B), k34_substut1(A, B)), k22_qc_lang1(A, k33_substut1(A, B)))))  &  ( ~ (r2_tarski(k21_qc_lang1(A, k33_substut1(A, B)), k10_xtuple_0(k7_substut1(A, k21_qc_lang1(A, k33_substut1(A, B)), k33_substut1(A, B), k34_substut1(A, B)))))  => k35_substut1(A, B)=k21_qc_lang1(A, k33_substut1(A, B))) ) ) ) ) ) ).
fof(d5_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_sublemma(B, A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  =>  (! [C] :  (m1_substut1(C, A, B) =>  (v3_substut1(B, A) => k9_sublemma(A, B, C)=k24_substut1(A, B, C)) ) ) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k11_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k13_substut1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_finset_1(B) & m1_subset_1(B, k1_substut1(A)))  & m1_subset_1(C, k9_qc_lang1(A))) )  => m1_subset_1(k13_substut1(A, B, C), k1_qc_lang1(A))) ) ).
fof(dt_k15_qc_lang1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k9_qc_lang1(A))) )  => m1_subset_1(k15_qc_lang1(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k16_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k16_substut1(A))) ) ) ).
fof(dt_k18_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k16_substut1(A)))  => m1_subset_1(k18_substut1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k19_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k16_substut1(A)))  => m1_subset_1(k19_substut1(A, B), k1_substut1(A))) ) ).
fof(dt_k1_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k1_qc_lang1(A))) ) ) ).
fof(dt_k1_substut1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k21_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m2_subset_1(k21_qc_lang1(A, B), k2_qc_lang1(A), k3_qc_lang1(A))) ) ).
fof(dt_k22_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k22_qc_lang1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k22_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  => m1_subset_1(k22_substut1(A, B), k16_substut1(A))) ) ).
fof(dt_k23_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  => m2_subset_1(k23_substut1(A, B), k2_qc_lang1(A), k3_qc_lang1(A))) ) ).
fof(dt_k24_substut1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))) & m1_substut1(C, A, B)) )  => m1_subset_1(k24_substut1(A, B, C), k16_substut1(A))) ) ).
fof(dt_k2_qc_lang1, axiom, $true).
fof(dt_k2_qc_lang3, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k1_qc_lang1(A)))  => m2_subset_1(k2_qc_lang3(A, B), k2_qc_lang1(A), k3_qc_lang1(A))) ) ).
fof(dt_k2_sublemma, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k38_substut1(A)))  => m2_subset_1(k2_sublemma(A, B), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k32_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k16_substut1(A)))  => m1_subset_1(k32_substut1(A, B), k2_zfmisc_1(k9_qc_lang1(A), k1_substut1(A)))) ) ).
fof(dt_k33_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k9_qc_lang1(A), k1_substut1(A))))  => m1_subset_1(k33_substut1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k34_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k9_qc_lang1(A), k1_substut1(A))))  => m1_subset_1(k34_substut1(A, B), k1_substut1(A))) ) ).
fof(dt_k35_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k9_qc_lang1(A), k1_substut1(A))))  => m2_subset_1(k35_substut1(A, B), k2_qc_lang1(A), k3_qc_lang1(A))) ) ).
fof(dt_k38_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k38_substut1(A), k1_zfmisc_1(k16_substut1(A)))) ) ).
fof(dt_k3_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_cqc_lang(A), k1_zfmisc_1(k9_qc_lang1(A)))) ) ).
fof(dt_k3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_qc_lang1(A), k1_zfmisc_1(k2_qc_lang1(A)))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k7_sublemma, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k38_substut1(A)) & m1_subset_1(C, k3_qc_lang1(A))) )  =>  (v1_sublemma(k7_sublemma(A, B, C), A) & m1_subset_1(k7_sublemma(A, B, C), k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A)))) ) ) ).
fof(dt_k7_substut1, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) &  (m1_subset_1(C, k9_qc_lang1(A)) & m1_subset_1(D, k1_substut1(A))) ) )  =>  (v1_finset_1(k7_substut1(A, B, C, D)) & m1_subset_1(k7_substut1(A, B, C, D), k1_substut1(A))) ) ) ).
fof(dt_k8_sublemma, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  (v1_sublemma(B, A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A)))) )  => m2_subset_1(k8_sublemma(A, B), k16_substut1(A), k38_substut1(A))) ) ).
fof(dt_k9_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k9_qc_lang1(A))) ) ) ).
fof(dt_k9_sublemma, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_sublemma(B, A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  & m1_substut1(C, A, B)) )  => m2_subset_1(k9_sublemma(A, B, C), k16_substut1(A), k38_substut1(A))) ) ).
fof(dt_m1_qc_lang1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  =>  (! [C] :  (m1_substut1(C, A, B) => m1_subset_1(C, k1_substut1(A))) ) ) ) ).
fof(dt_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, A)) ) ) ) ).
fof(existence_m1_qc_lang1, axiom,  (? [A] : m1_qc_lang1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m1_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  =>  (? [C] : m1_substut1(C, A, B)) ) ) ).
fof(existence_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(fc10_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  => v1_setfam_1(k10_xtuple_0(A))) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc1_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k1_qc_lang1(A))) ) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k1_substut1(A))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc2_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_cqc_lang(A))) ) ) ).
fof(fc2_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k2_qc_lang1(A))) ) ) ).
fof(fc2_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) => v4_funct_1(k1_substut1(A))) ) ).
fof(fc3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_qc_lang1(A))) ) ) ).
fof(fc4_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ( ~ (v1_xboole_0(k16_substut1(A)))  & v1_substut1(k16_substut1(A), A)) ) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc7_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k38_substut1(A))) ) ) ).
fof(fc9_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k10_xtuple_0(A))) ) ) ).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (? [B] :  (m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))) & v1_sublemma(B, A)) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (? [B] :  (m1_subset_1(B, k1_substut1(A)) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (? [B] :  ( ~ (v1_xboole_0(B))  & v1_substut1(B, A)) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_xtuple_0, axiom,  (! [A, B] : k1_xtuple_0(k4_tarski(A, B))=A) ).
fof(rd2_xtuple_0, axiom,  (! [A, B] : k2_xtuple_0(k4_tarski(A, B))=B) ).
fof(rd3_xtuple_0, axiom,  (! [A] :  (v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(redefinition_k11_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k11_cqc_lang(A, B, C)=k15_qc_lang1(A, B, C)) ) ).
fof(redefinition_k18_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k16_substut1(A)))  => k18_substut1(A, B)=k1_xtuple_0(B)) ) ).
fof(redefinition_k19_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k16_substut1(A)))  => k19_substut1(A, B)=k2_xtuple_0(B)) ) ).
fof(redefinition_k22_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  => k22_substut1(A, B)=k1_xtuple_0(B)) ) ).
fof(redefinition_k23_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  => k23_substut1(A, B)=k2_xtuple_0(B)) ) ).
fof(redefinition_k2_sublemma, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k38_substut1(A)))  => k2_sublemma(A, B)=k1_xtuple_0(B)) ) ).
fof(redefinition_k33_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k9_qc_lang1(A), k1_substut1(A))))  => k33_substut1(A, B)=k1_xtuple_0(B)) ) ).
fof(redefinition_k34_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k9_qc_lang1(A), k1_substut1(A))))  => k34_substut1(A, B)=k2_xtuple_0(B)) ) ).
fof(redefinition_k7_sublemma, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k38_substut1(A)) & m1_subset_1(C, k3_qc_lang1(A))) )  => k7_sublemma(A, B, C)=k4_tarski(B, C)) ) ).
fof(redefinition_k8_sublemma, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  (v1_sublemma(B, A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A)))) )  => k8_sublemma(A, B)=k1_xtuple_0(B)) ) ).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t26_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))) =>  (! [C] :  (m1_substut1(C, A, B) =>  (v3_substut1(B, A) =>  (k18_substut1(A, k24_substut1(A, B, C))=k15_qc_lang1(A, k23_substut1(A, B), k18_substut1(A, k22_substut1(A, B))) & k19_substut1(A, k24_substut1(A, B, C))=C) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_qc_lang2, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [C] :  (m1_subset_1(C, k9_qc_lang1(A)) =>  (k21_qc_lang1(A, k15_qc_lang1(A, B, C))=B & k22_qc_lang1(A, k15_qc_lang1(A, B, C))=C) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
